Oncolytic virotherapy for tumours following a Gompertz growth law

TL;DR

This paper develops a mathematical model of oncolytic virotherapy for tumors with Gompertz growth, revealing complex dynamics like oscillations and bistability, and highlighting conditions for effective tumor eradication.

Contribution

It introduces a novel nonlinear model incorporating Gompertz tumor growth and analyzes stability, bifurcations, and treatment strategies, providing new insights into optimal virotherapy parameters.

Findings

Complete eradication depends on matching viral and tumor growth rates.

High initial viral doses or highly infective viruses do not guarantee success.

Low viral loads can sometimes be more effective than high doses.

Abstract

We present a mathematical model describing oncolytic virotherapy treatment of a tumour that proliferates according to a Gompertz growth function. We present local stability analysis and bifurcation plots for relevant model parameters to investigate the typical dynamical regimes that the model allows. The model shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly infective virus do not universally result in successful strategies for eradication. Further, the use of additional, boosting injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus.